Mathematical Programming with Data Perturbations II, Second Edition

Mathematical Programming with Data Perturbations II, Second Edition
Author: Fiacco
Publisher: CRC Press
Total Pages: 174
Release: 2020-09-24
Genre: Mathematics
ISBN: 1000153436

This book presents theoretical results, including an extension of constant rank and implicit function theorems, continuity and stability bounds results for infinite dimensional problems, and the interrelationship between optimal value conditions and shadow prices for stable and unstable programs.

Mathematical Programming with Data Perturbations

Mathematical Programming with Data Perturbations
Author: Anthony V. Fiacco
Publisher: CRC Press
Total Pages: 460
Release: 1997-09-19
Genre: Mathematics
ISBN: 9780824700591

Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.

Perturbation Analysis of Optimization Problems

Perturbation Analysis of Optimization Problems
Author: J.Frederic Bonnans
Publisher: Springer Science & Business Media
Total Pages: 626
Release: 2000-05-11
Genre: Mathematics
ISBN: 9780387987057

A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.

Mathematical Programming with Data Perturbations

Mathematical Programming with Data Perturbations
Author: Anthony V. Fiacco
Publisher: CRC Press
Total Pages: 460
Release: 2020-09-24
Genre: Mathematics
ISBN: 1000153665

Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.

Mathematical Programming with Data Perturbations II, Second Edition

Mathematical Programming with Data Perturbations II, Second Edition
Author: Fiacco
Publisher: CRC Press
Total Pages: 174
Release: 1983-01-24
Genre: Mathematics
ISBN: 9780824717896

Theorem of constant rank to lipschitzian maps; Lipschitzian perturbations of infinite optimization problems; On the continuity of the optimum set in parametric semiinfinite programming; Optimality conditions and shadow prices; Optimal value continuity and differential stability bounds under the mangasarian-fromovitz constraint qualification; Iteration and sensitivity for a nonlinear spatial equilibrium problem; A sensitivity analysis approach to iteration skipping in the harmonic mean algorithm; Least squares optimization with implicit model equations.

Stochastic Recursive Algorithms for Optimization

Stochastic Recursive Algorithms for Optimization
Author: S. Bhatnagar
Publisher: Springer
Total Pages: 310
Release: 2012-08-11
Genre: Technology & Engineering
ISBN: 1447142853

Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from similarly diverse backgrounds: workers in relevant areas of computer science, control engineering, management science, applied mathematics, industrial engineering and operations research will find the content of value.

Robust Data Mining

Robust Data Mining
Author: Petros Xanthopoulos
Publisher: Springer Science & Business Media
Total Pages: 67
Release: 2012-11-28
Genre: Mathematics
ISBN: 1441998780

Data uncertainty is a concept closely related with most real life applications that involve data collection and interpretation. Examples can be found in data acquired with biomedical instruments or other experimental techniques. Integration of robust optimization in the existing data mining techniques aim to create new algorithms resilient to error and noise. This work encapsulates all the latest applications of robust optimization in data mining. This brief contains an overview of the rapidly growing field of robust data mining research field and presents the most well known machine learning algorithms, their robust counterpart formulations and algorithms for attacking these problems. This brief will appeal to theoreticians and data miners working in this field.